Structure Refinement: LBCO, HRPT¶

This example demonstrates how to use the EasyDiffraction API in a simplified, user-friendly manner that closely follows the GUI workflow for a Rietveld refinement of La0.5Ba0.5CoO3 crystal structure using constant wavelength neutron powder diffraction data from HRPT at PSI.

It is intended for users with minimal programming experience who want to learn how to perform standard crystal structure fitting using diffraction data. This script covers creating a project, adding crystal structures and experiments, performing analysis, and refining parameters.

Only a single import of easydiffraction is required, and all operations are performed through high-level components of the project object, such as project.structures, project.experiments, and project.analysis. The project object is the main container for all information.

Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Step 1: Create a Project¶

This section explains how to create a project and define its metadata.

Create Project¶

In [3]:

project = ed.Project(name='lbco_hrpt')

project = ed.Project(name='lbco_hrpt')

Set Project Metadata¶

In [4]:

project.info.title = 'La0.5Ba0.5CoO3 at HRPT@PSI'
project.info.description = """This project demonstrates a standard
refinement of La0.5Ba0.5CoO3, which crystallizes in a perovskite-type
structure, using neutron powder diffraction data collected in constant
wavelength mode at the HRPT diffractometer (PSI)."""

project.info.title = 'La0.5Ba0.5CoO3 at HRPT@PSI' project.info.description = """This project demonstrates a standard refinement of La0.5Ba0.5CoO3, which crystallizes in a perovskite-type structure, using neutron powder diffraction data collected in constant wavelength mode at the HRPT diffractometer (PSI)."""

Show Project Metadata as CIF¶

In [5]:

project.info.show_as_cif()

project.info.show_as_cif()

Project 📦 'lbco_hrpt' info as CIF

	CIF
1	_project.id lbco_hrpt
2	_project.title 'La0.5Ba0.5CoO3 at HRPT@PSI'
3	_project.description
4	;
5	This project demonstrates a standard refinement of La0.5Ba0.5CoO3, which crystallizes in a perovskite-type structure, using neutron powder diffraction data collected in constant wavelength mode at the HRPT diffractometer (PSI).
6	;
7	_project.created '06 May 2026 15:18:28'
8	_project.last_modified '06 May 2026 15:18:28'

Save Project¶

When saving the project for the first time, you need to specify the directory path. In the example below, the project is saved to a temporary location defined by the system.

In [6]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

├── 📁 experiments/

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Set Up Data Plotter¶

Show supported plotting engines.

In [7]:

project.display.plotter.show_supported_engines()

project.display.plotter.show_supported_engines()

Supported engines

	Engine	Description
1	asciichartpy	Console ASCII line charts
2	plotly	Interactive browser-based graphing library

Show current plotting configuration.

In [8]:

project.display.plotter.show_config()

project.display.plotter.show_config()

Current plotter configuration

	Parameter	Value
1	Plotting engine	plotly
2	x-axis limits	[-inf, inf]
3	Chart height	25

Step 2: Define Structure¶

This section shows how to add structures and modify their parameters.

Add Structure¶

In [9]:

project.structures.create(name='lbco')

project.structures.create(name='lbco')

Show Defined Structures¶

Show the names of the crystal structures added. These names are used to access the structure using the syntax: project.structures[name]. All structure parameters can be accessed via the project object.

In [10]:

project.structures.show_names()

project.structures.show_names()

Defined structures 🧩

['lbco']

Set Space Group¶

Modify the default space group parameters.

In [11]:

project.structures['lbco'].space_group.name_h_m = 'P m -3 m'
project.structures['lbco'].space_group.it_coordinate_system_code = '1'

project.structures['lbco'].space_group.name_h_m = 'P m -3 m' project.structures['lbco'].space_group.it_coordinate_system_code = '1'

Set Unit Cell¶

Modify the default unit cell parameters.

In [12]:

project.structures['lbco'].cell.length_a = 3.88

project.structures['lbco'].cell.length_a = 3.88

Set Atom Sites¶

Add atom sites to the structure.

In [13]:

project.structures['lbco'].atom_sites.create(
    label='La',
    type_symbol='La',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    adp_iso=0.5,
    occupancy=0.5,
)
project.structures['lbco'].atom_sites.create(
    label='Ba',
    type_symbol='Ba',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    adp_iso=0.5,
    occupancy=0.5,
)
project.structures['lbco'].atom_sites.create(
    label='Co',
    type_symbol='Co',
    fract_x=0.5,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='b',
    adp_iso=0.5,
)
project.structures['lbco'].atom_sites.create(
    label='O',
    type_symbol='O',
    fract_x=0,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='c',
    adp_iso=0.5,
)

project.structures['lbco'].atom_sites.create( label='La', type_symbol='La', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', adp_iso=0.5, occupancy=0.5, ) project.structures['lbco'].atom_sites.create( label='Ba', type_symbol='Ba', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', adp_iso=0.5, occupancy=0.5, ) project.structures['lbco'].atom_sites.create( label='Co', type_symbol='Co', fract_x=0.5, fract_y=0.5, fract_z=0.5, wyckoff_letter='b', adp_iso=0.5, ) project.structures['lbco'].atom_sites.create( label='O', type_symbol='O', fract_x=0, fract_y=0.5, fract_z=0.5, wyckoff_letter='c', adp_iso=0.5, )

Show Structure as CIF¶

In [14]:

project.structures['lbco'].show_as_cif()

project.structures['lbco'].show_as_cif()

Structure 🧩 'lbco' as cif

	CIF
1	data_lbco
2
3	_cell.length_a 3.88
4	_cell.length_b 3.88
5	_cell.length_c 3.88
6	_cell.angle_alpha 90.
7	_cell.angle_beta 90.
8	_cell.angle_gamma 90.
9
10	_space_group.name_H-M_alt "P m -3 m"
11	_space_group.IT_coordinate_system_code 1
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.B_iso_or_equiv
22	_atom_site.adp_type
23	La La 0. 0. 0. a 0.5 0.5 Biso
24	Ba Ba 0. 0. 0. a 0.5 0.5 Biso
25	Co Co 0.5 0.5 0.5 b 1. 0.5 Biso
26	O O 0. 0.5 0.5 c 1. 0.5 Biso
27

Show Structure Structure¶

In [15]:

project.structures['lbco'].show()

project.structures['lbco'].show()

Structure 🧩 'lbco'

Not implemented yet.

Save Project State¶

Save the project state after adding the structure. This ensures that all changes are stored and can be accessed later. The project state is saved in the directory specified during project creation.

In [16]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Step 3: Define Experiment¶

This section shows how to add experiments, configure their parameters, and link the structures defined in the previous step.

Download Measured Data¶

Download the data file from the EasyDiffraction repository on GitHub.

In [17]:

data_path = ed.download_data(id=3, destination='data')

data_path = ed.download_data(id=3, destination='data')

Getting data...

Data #3: La0.5Ba0.5CoO3, HRPT (PSI), 300 K

✅ Data #3 already present at 'data/ed-3.xye'. Keeping existing file.

Add Diffraction Experiment¶

In [18]:

project.experiments.add_from_data_path(
    name='hrpt',
    data_path=data_path,
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
)

project.experiments.add_from_data_path( name='hrpt', data_path=data_path, sample_form='powder', beam_mode='constant wavelength', radiation_probe='neutron', )

Data loaded successfully

Experiment 🔬 'hrpt'. Number of data points: 3098.

Show Defined Experiments¶

In [19]:

project.experiments.show_names()

project.experiments.show_names()

Defined experiments 🔬

['hrpt']

Show Measured Data¶

In [20]:

project.display.plotter.plot_meas(expt_name='hrpt')

project.display.plotter.plot_meas(expt_name='hrpt')

Warning: No linked phases defined. Returning empty pattern.

Set Instrument¶

Modify the default instrument parameters.

In [21]:

project.experiments['hrpt'].instrument.setup_wavelength = 1.494
project.experiments['hrpt'].instrument.calib_twotheta_offset = 0.6

project.experiments['hrpt'].instrument.setup_wavelength = 1.494 project.experiments['hrpt'].instrument.calib_twotheta_offset = 0.6

Set Peak Profile¶

Show supported peak profile types.

In [22]:

project.experiments['hrpt'].show_peak_profile_types()

project.experiments['hrpt'].show_peak_profile_types()

Peak profile types

		Type	Description
1	*	pseudo-voigt	CWL pseudo-Voigt profile
2		pseudo-voigt + empirical asymmetry	CWL pseudo-Voigt profile with empirical asymmetry correction.

Select the desired peak profile type.

In [23]:

project.experiments['hrpt'].peak_profile_type = 'pseudo-voigt'

project.experiments['hrpt'].peak_profile_type = 'pseudo-voigt'

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

Peak profile type for experiment 'hrpt' changed to

pseudo-voigt

Modify default peak profile parameters.

In [24]:

project.experiments['hrpt'].peak.broad_gauss_u = 0.1
project.experiments['hrpt'].peak.broad_gauss_v = -0.1
project.experiments['hrpt'].peak.broad_gauss_w = 0.1
project.experiments['hrpt'].peak.broad_lorentz_x = 0
project.experiments['hrpt'].peak.broad_lorentz_y = 0.1

project.experiments['hrpt'].peak.broad_gauss_u = 0.1 project.experiments['hrpt'].peak.broad_gauss_v = -0.1 project.experiments['hrpt'].peak.broad_gauss_w = 0.1 project.experiments['hrpt'].peak.broad_lorentz_x = 0 project.experiments['hrpt'].peak.broad_lorentz_y = 0.1

Set Background¶

Show supported background types.

In [25]:

project.experiments['hrpt'].show_background_types()

project.experiments['hrpt'].show_background_types()

Background types

		Type	Description
1		chebyshev	Chebyshev polynomial background
2	*	line-segment	Linear interpolation between points

Select the desired background type.

In [26]:

project.experiments['hrpt'].background_type = 'line-segment'

project.experiments['hrpt'].background_type = 'line-segment'

Background type for experiment 'hrpt' already set to

line-segment

Add background points.

In [27]:

project.experiments['hrpt'].background.create(id='10', x=10, y=170)
project.experiments['hrpt'].background.create(id='30', x=30, y=170)
project.experiments['hrpt'].background.create(id='50', x=50, y=170)
project.experiments['hrpt'].background.create(id='110', x=110, y=170)
project.experiments['hrpt'].background.create(id='165', x=165, y=170)

project.experiments['hrpt'].background.create(id='10', x=10, y=170) project.experiments['hrpt'].background.create(id='30', x=30, y=170) project.experiments['hrpt'].background.create(id='50', x=50, y=170) project.experiments['hrpt'].background.create(id='110', x=110, y=170) project.experiments['hrpt'].background.create(id='165', x=165, y=170)

Show current background points.

In [28]:

project.experiments['hrpt'].background.show()

project.experiments['hrpt'].background.show()

Line-segment background points

	X	Intensity
1	10	170
2	30	170
3	50	170
4	110	170
5	165	170

Set Linked Phases¶

Link the structure defined in the previous step to the experiment.

In [29]:

project.experiments['hrpt'].linked_phases.create(id='lbco', scale=10.0)

project.experiments['hrpt'].linked_phases.create(id='lbco', scale=10.0)

Show Experiment as CIF¶

In [30]:

project.experiments['hrpt'].show_as_cif()

project.experiments['hrpt'].show_as_cif()

Experiment 🔬 'hrpt' as cif

	CIF
1	data_hrpt
2
3	_expt_type.sample_form powder
4	_expt_type.beam_mode "constant wavelength"
5	_expt_type.radiation_probe neutron
6	_expt_type.scattering_type bragg
7
8	_diffrn.ambient_temperature ?
9	_diffrn.ambient_pressure ?
10	_diffrn.ambient_magnetic_field ?
11	_diffrn.ambient_electric_field ?
12
13	_calculation.calculator_type cryspy
14
15	_peak.broad_gauss_u 0.1
16	_peak.broad_gauss_v -0.1
17	_peak.broad_gauss_w 0.1
18	_peak.broad_lorentz_x 0.
19	_peak.broad_lorentz_y 0.1
20	_peak.profile_type cwl-pseudo-voigt
21
22	_instr.wavelength 1.494
23	_instr.2theta_offset 0.6
24
25	loop_
26	_pd_phase_block.id
27	_pd_phase_block.scale
28	lbco 10.
29
30
31
32	loop_
33	_pd_proc.2theta_scan
34	_pd_data.point_id
35	_pd_proc.d_spacing
36	_pd_meas.intensity_total
37	_pd_meas.intensity_total_su
38	_pd_calc.intensity_total
39	_pd_calc.intensity_bkg
40	_pd_data.refinement_status
41	10. 1 8.57086379 167. 12.6 172.32780248 170. incl
42	10.05 2 8.52833125 157. 12.5 172.30859914 170. incl
43	10.1 3 8.48622036 187. 13.3 172.28969336 170. incl
44	10.15 4 8.4445249 197. 14. 172.27107915 170. incl
45	10.2 5 8.40323875 164. 12.5 172.25275064 170. incl
46	10.25 6 8.36235592 171. 13. 172.23470212 170. incl
47	10.3 7 8.32187055 190. 13.4 172.21692803 170. incl
48	10.35 8 8.28177687 182. 13.5 172.19942295 170. incl
49	10.4 9 8.24206922 166. 12.6 172.18218159 170. incl
50	10.45 10 8.20274208 203. 14.3 172.1651988 170. incl
51	...
52	164.4 3089 0.75397591 202. 18.5 172.60037118 170. incl
53	164.45 3090 0.75393091 178. 20.4 172.59695823 170. incl
54	164.5 3091 0.75388607 153. 18. 172.59381336 170. incl
55	164.55 3092 0.75384138 197. 25.3 172.59093099 170. incl
56	164.6 3093 0.75379684 153. 20.7 172.58830579 170. incl
57	164.65 3094 0.75375244 173. 30.1 172.58593268 170. incl
58	164.7 3095 0.75370819 187. 27.9 172.5838068 170. incl
59	164.75 3096 0.7536641 175. 38.2 172.58192354 170. incl
60	164.8 3097 0.75362015 168. 30.9 172.58027848 170. incl
61	164.85 3098 0.75357634 109. 41.2 172.57886743 170. incl
62
63	loop_
64	_pd_background.id
65	_pd_background.line_segment_X
66	_pd_background.line_segment_intensity
67	10 10. 170.
68	30 30. 170.
69	50 50. 170.
70	110 110. 170.
71	165 165. 170.
72
73	loop_
74	_refln.id
75	_refln.phase_id
76	_refln.d_spacing
77	_refln.sin_theta_over_lambda
78	_refln.index_h
79	_refln.index_k
80	_refln.index_l
81	_refln.f_calc
82	_refln.f_squared_calc
83	_refln.two_theta
84	1 lbco 3.88 0.12886598 1. 0. 0. 0.16244556 0.02638856 22.80044453
85	2 lbco 2.74357431 0.18224402 1. 1. 0. 0.32869596 0.10804103 32.19908449
86	3 lbco 2.24011904 0.22320242 1. 1. 1. 2.1043237 4.42817823 39.5583744
87	4 lbco 1.94 0.25773196 2. 0. 0. 2.56865501 6.59798858 45.89388073
88	5 lbco 1.73518875 0.28815309 2. 1. 0. 0.15713889 0.02469263 51.5986821
89	6 lbco 1.58400337 0.31565589 2. 1. 1. 0.31795832 0.10109749 56.8751008
90	7 lbco 1.37178716 0.36448803 2. 2. 0. 2.48474376 6.17395156 66.58716829
91	8 lbco 1.29333333 0.38659794 2. 2. 1. 0.15200557 0.02310569 71.16064798
92	9 lbco 1.29333333 0.38659794 3. 0. 0. 0.15200557 0.02310569 71.16064798
93	10 lbco 1.22696373 0.40751001 3. 1. 0. 0.30757145 0.0946002 75.60845321
94	...
95	19 lbco 0.91452477 0.54673205 4. 1. 1. 0.28780456 0.08283147 110.13497669
96	20 lbco 0.89013305 0.56171378 3. 3. 1. 1.84253549 3.39493703 114.71155759
97	21 lbco 0.86759438 0.57630618 4. 2. 0. 2.24910171 5.0584585 119.45842061
98	22 lbco 0.84668541 0.59053811 4. 2. 1. 0.13759004 0.01893102 124.43335485
99	23 lbco 0.82721878 0.60443502 3. 3. 2. 0.27840274 0.07750809 129.7174128
100	24 lbco 0.79200168 0.63131179 4. 2. 2. 2.17562943 4.73336341 141.78522183
101	25 lbco 0.776 0.6443299 4. 3. 0. 0.13309533 0.01771437 149.17338292
102	26 lbco 0.776 0.6443299 5. 0. 0. 0.13309533 0.01771437 149.17338292
103	27 lbco 0.7609306 0.65709014 4. 3. 1. 0.26930805 0.07252683 158.63936579
104	28 lbco 0.7609306 0.65709014 5. 1. 0. 0.26930805 0.07252683 158.63936579

Save Project State¶

In [31]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Step 4: Perform Analysis¶

This section explains the analysis process, including how to set up calculation and fitting engines.

Set Calculator¶

Show supported calculation engines for this experiment.

In [32]:

project.experiments['hrpt'].calculation.show_calculator_types()

project.experiments['hrpt'].calculation.show_calculator_types()

Calculator types

		Type	Description
1		crysfml	CrysFML library for crystallographic calculations
2	*	cryspy	CrysPy library for crystallographic calculations

Select the desired calculation engine.

In [33]:

project.experiments['hrpt'].calculation.calculator_type = 'cryspy'

project.experiments['hrpt'].calculation.calculator_type = 'cryspy'

Calculator for experiment 'hrpt' already set to

cryspy

Show Calculated Data¶

In [34]:

project.display.plotter.plot_calc(expt_name='hrpt')

project.display.plotter.plot_calc(expt_name='hrpt')

Plot Measured vs Calculated¶

In [35]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [36]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Show Parameters¶

Show all parameters of the project.

In [37]:

# project.analysis.display.all_params()

# project.analysis.display.all_params()

Show all fittable parameters.

In [38]:

project.analysis.display.fittable_params()

project.analysis.display.fittable_params()

Fittable parameters for all structures (🧩 data blocks)

	datablock	category	entry	parameter	value	uncertainty	units	free
1	lbco	cell		length_a	3.88000		Å	False
2	lbco	cell		length_b	3.88000		Å	False
3	lbco	cell		length_c	3.88000		Å	False
4	lbco	cell		angle_alpha	90.00000		deg	False
5	lbco	cell		angle_beta	90.00000		deg	False
6	lbco	cell		angle_gamma	90.00000		deg	False
7	lbco	atom_site	La	fract_x	0.00000			False
8	lbco	atom_site	La	fract_y	0.00000			False
9	lbco	atom_site	La	fract_z	0.00000			False
10	lbco	atom_site	La	occupancy	0.50000			False
11	lbco	atom_site	La	adp_iso	0.50000		Ų	False
12	lbco	atom_site	Ba	fract_x	0.00000			False
13	lbco	atom_site	Ba	fract_y	0.00000			False
14	lbco	atom_site	Ba	fract_z	0.00000			False
15	lbco	atom_site	Ba	occupancy	0.50000			False
16	lbco	atom_site	Ba	adp_iso	0.50000		Ų	False
17	lbco	atom_site	Co	fract_x	0.50000			False
18	lbco	atom_site	Co	fract_y	0.50000			False
19	lbco	atom_site	Co	fract_z	0.50000			False
20	lbco	atom_site	Co	occupancy	1.00000			False
21	lbco	atom_site	Co	adp_iso	0.50000		Ų	False
22	lbco	atom_site	O	fract_x	0.00000			False
23	lbco	atom_site	O	fract_y	0.50000			False
24	lbco	atom_site	O	fract_z	0.50000			False
25	lbco	atom_site	O	occupancy	1.00000			False
26	lbco	atom_site	O	adp_iso	0.50000		Ų	False

Fittable parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	units	free
1	hrpt	linked_phases	lbco	scale	10.00000			False
2	hrpt	peak		broad_gauss_u	0.10000		deg²	False
3	hrpt	peak		broad_gauss_v	-0.10000		deg²	False
4	hrpt	peak		broad_gauss_w	0.10000		deg²	False
5	hrpt	peak		broad_lorentz_x	0.00000		deg	False
6	hrpt	peak		broad_lorentz_y	0.10000		deg	False
7	hrpt	instrument		wavelength	1.49400		Å	False
8	hrpt	instrument		twotheta_offset	0.60000		deg	False
9	hrpt	background	10	y	170.00000			False
10	hrpt	background	30	y	170.00000			False
11	hrpt	background	50	y	170.00000			False
12	hrpt	background	110	y	170.00000			False
13	hrpt	background	165	y	170.00000			False

Show only free parameters.

In [39]:

project.analysis.display.free_params()

project.analysis.display.free_params()

⚠️ No free parameters found.                                                                                                      

Show how to access parameters in the code.

In [40]:

# project.analysis.display.how_to_access_parameters()

# project.analysis.display.how_to_access_parameters()

Set Fit Mode¶

Show supported fit modes.

In [41]:

project.analysis.fit.show_modes()

project.analysis.fit.show_modes()

Fit modes

		Type	Description
1	*	single	Independent fitting of each experiment

Select desired fit mode.

In [42]:

project.analysis.fit.mode = 'single'

project.analysis.fit.mode = 'single'

Set Minimizer¶

Show supported fitting engines.

In [43]:

project.analysis.fit.show_minimizer_types()

project.analysis.fit.show_minimizer_types()

Minimizer types

		Type	Description
1		bumps	Bumps library using the default Levenberg-Marquardt method
2		bumps (amoeba)	Bumps library with Nelder-Mead simplex method
3		bumps (de)	Bumps library with differential evolution method
4		bumps (lm)	Bumps library with Levenberg-Marquardt method
5		dfols	DFO-LS library for derivative-free least-squares optimization
6		lmfit	LMFIT library using the default Levenberg-Marquardt least squares method
7		lmfit (least_squares)	LMFIT library with SciPy's trust region reflective algorithm
8	*	lmfit (leastsq)	LMFIT library with Levenberg-Marquardt least squares method

Select desired fitting engine.

In [44]:

project.analysis.fit.minimizer_type = 'lmfit'

project.analysis.fit.minimizer_type = 'lmfit'

Current minimizer changed to

lmfit

Perform Fit 1/5¶

Set structure parameters to be refined.

In [45]:

project.structures['lbco'].cell.length_a.free = True

project.structures['lbco'].cell.length_a.free = True

Set experiment parameters to be refined.

In [46]:

project.experiments['hrpt'].linked_phases['lbco'].scale.free = True
project.experiments['hrpt'].instrument.calib_twotheta_offset.free = True
project.experiments['hrpt'].background['10'].y.free = True
project.experiments['hrpt'].background['30'].y.free = True
project.experiments['hrpt'].background['50'].y.free = True
project.experiments['hrpt'].background['110'].y.free = True
project.experiments['hrpt'].background['165'].y.free = True

project.experiments['hrpt'].linked_phases['lbco'].scale.free = True project.experiments['hrpt'].instrument.calib_twotheta_offset.free = True project.experiments['hrpt'].background['10'].y.free = True project.experiments['hrpt'].background['30'].y.free = True project.experiments['hrpt'].background['50'].y.free = True project.experiments['hrpt'].background['110'].y.free = True project.experiments['hrpt'].background['165'].y.free = True

Show free parameters after selection.

In [47]:

project.analysis.display.free_params()

project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	lbco	cell		length_a	3.88000		-inf	inf	Å
2	hrpt	linked_phases	lbco	scale	10.00000		-inf	inf
3	hrpt	instrument		twotheta_offset	0.60000		-inf	inf	deg
4	hrpt	background	10	y	170.00000		-inf	inf
5	hrpt	background	30	y	170.00000		-inf	inf
6	hrpt	background	50	y	170.00000		-inf	inf
7	hrpt	background	110	y	170.00000		-inf	inf
8	hrpt	background	165	y	170.00000		-inf	inf

Run Fitting¶

In [48]:

project.analysis.fit()
project.analysis.display.fit_results()

project.analysis.fit() project.analysis.display.fit_results()

Standard fitting

📋 Using experiment 🔬 'hrpt' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	164.59
2	12	33.43	79.7% ↓
3	21	13.22	60.4% ↓
4	30	5.78	56.3% ↓
5	39	3.15	45.6% ↓
6	77	3.14

🏆 Best goodness-of-fit (reduced χ²) is 3.14 at iteration 69

✅ Fitting complete.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 4.42 seconds

📏 Goodness-of-fit (reduced χ²): 3.14

📏 R-factor (Rf): 8.42%

📏 R-factor squared (Rf²): 11.79%

📏 Weighted R-factor (wR): 11.62%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8800	3.8910	0.0001	Å	0.28 % ↑
2	hrpt	linked_phases	lbco	scale	10.0000	7.3409	0.0350		26.59 % ↓
3	hrpt	instrument		twotheta_offset	0.6000	0.6243	0.0018	deg	4.05 % ↑
4	hrpt	background	10	y	170.0000	167.7066	2.1300		1.35 % ↓
5	hrpt	background	30	y	170.0000	166.0338	1.5404		2.33 % ↓
6	hrpt	background	50	y	170.0000	169.9495	1.1025		0.03 % ↓
7	hrpt	background	110	y	170.0000	170.0802	0.9788		0.05 % ↑
8	hrpt	background	165	y	170.0000	179.6656	1.3289		5.69 % ↑

Plot Measured vs Calculated¶

In [49]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [50]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Save Project State¶

In [51]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 2/5¶

Set more parameters to be refined.

In [52]:

project.experiments['hrpt'].peak.broad_gauss_u.free = True
project.experiments['hrpt'].peak.broad_gauss_v.free = True
project.experiments['hrpt'].peak.broad_gauss_w.free = True
project.experiments['hrpt'].peak.broad_lorentz_y.free = True

project.experiments['hrpt'].peak.broad_gauss_u.free = True project.experiments['hrpt'].peak.broad_gauss_v.free = True project.experiments['hrpt'].peak.broad_gauss_w.free = True project.experiments['hrpt'].peak.broad_lorentz_y.free = True

Show free parameters after selection.

In [53]:

project.analysis.display.free_params()

project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	lbco	cell		length_a	3.89099	0.00006	-inf	inf	Å
2	hrpt	linked_phases	lbco	scale	7.34088	0.03496	-inf	inf
3	hrpt	peak		broad_gauss_u	0.10000		-inf	inf	deg²
4	hrpt	peak		broad_gauss_v	-0.10000		-inf	inf	deg²
5	hrpt	peak		broad_gauss_w	0.10000		-inf	inf	deg²
6	hrpt	peak		broad_lorentz_y	0.10000		-inf	inf	deg
7	hrpt	instrument		twotheta_offset	0.62432	0.00181	-inf	inf	deg
8	hrpt	background	10	y	167.70662	2.13004	-inf	inf
9	hrpt	background	30	y	166.03383	1.54041	-inf	inf
10	hrpt	background	50	y	169.94949	1.10249	-inf	inf
11	hrpt	background	110	y	170.08023	0.97879	-inf	inf
12	hrpt	background	165	y	179.66557	1.32895	-inf	inf

Run Fitting¶

In [54]:

project.analysis.fit()
project.analysis.display.fit_results()

project.analysis.fit() project.analysis.display.fit_results()

Standard fitting

📋 Using experiment 🔬 'hrpt' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	3.14
2	16	2.85	9.1% ↓
3	69	2.85

🏆 Best goodness-of-fit (reduced χ²) is 2.85 at iteration 68

✅ Fitting complete.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 3.58 seconds

📏 Goodness-of-fit (reduced χ²): 2.85

📏 R-factor (Rf): 8.30%

📏 R-factor squared (Rf²): 11.85%

📏 Weighted R-factor (wR): 11.91%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8910	3.8909	0.0001	Å	0.00 % ↓
2	hrpt	linked_phases	lbco	scale	7.3409	7.2120	0.0406		1.76 % ↓
3	hrpt	peak		broad_gauss_u	0.1000	0.0803	0.0047	deg²	19.74 % ↓
4	hrpt	peak		broad_gauss_v	-0.1000	-0.1029	0.0104	deg²	2.93 % ↑
5	hrpt	peak		broad_gauss_w	0.1000	0.1077	0.0051	deg²	7.66 % ↑
6	hrpt	peak		broad_lorentz_y	0.1000	0.0893	0.0032	deg	10.67 % ↓
7	hrpt	instrument		twotheta_offset	0.6243	0.6231	0.0017	deg	0.19 % ↓
8	hrpt	background	10	y	167.7066	167.5167	2.0311		0.11 % ↓
9	hrpt	background	30	y	166.0338	166.7627	1.4794		0.44 % ↑
10	hrpt	background	50	y	169.9495	170.8330	1.0808		0.52 % ↑
11	hrpt	background	110	y	170.0802	172.2546	0.9660		1.28 % ↑
12	hrpt	background	165	y	179.6656	180.6405	1.2737		0.54 % ↑

Plot Measured vs Calculated¶

In [55]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [56]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Save Project State¶

In [57]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 3/5¶

Set more parameters to be refined.

In [58]:

project.structures['lbco'].atom_sites['La'].adp_iso.free = True
project.structures['lbco'].atom_sites['Ba'].adp_iso.free = True
project.structures['lbco'].atom_sites['Co'].adp_iso.free = True
project.structures['lbco'].atom_sites['O'].adp_iso.free = True

project.structures['lbco'].atom_sites['La'].adp_iso.free = True project.structures['lbco'].atom_sites['Ba'].adp_iso.free = True project.structures['lbco'].atom_sites['Co'].adp_iso.free = True project.structures['lbco'].atom_sites['O'].adp_iso.free = True

Show free parameters after selection.

In [59]:

project.analysis.display.free_params()

project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	lbco	cell		length_a	3.89091	0.00005	-inf	inf	Å
2	lbco	atom_site	La	adp_iso	0.50000		-inf	inf	Ų
3	lbco	atom_site	Ba	adp_iso	0.50000		-inf	inf	Ų
4	lbco	atom_site	Co	adp_iso	0.50000		-inf	inf	Ų
5	lbco	atom_site	O	adp_iso	0.50000		-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	7.21199	0.04057	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08026	0.00472	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.10293	0.01036	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.10766	0.00515	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08933	0.00320	-inf	inf	deg
11	hrpt	instrument		twotheta_offset	0.62314	0.00167	-inf	inf	deg
12	hrpt	background	10	y	167.51669	2.03112	-inf	inf
13	hrpt	background	30	y	166.76268	1.47937	-inf	inf
14	hrpt	background	50	y	170.83305	1.08080	-inf	inf
15	hrpt	background	110	y	172.25458	0.96599	-inf	inf
16	hrpt	background	165	y	180.64054	1.27368	-inf	inf

Run Fitting¶

In [60]:

project.analysis.fit()
project.analysis.display.fit_results()

project.analysis.fit() project.analysis.display.fit_results()

Standard fitting

📋 Using experiment 🔬 'hrpt' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	2.85
2	28	2.28	19.9% ↓
3	45	1.62	28.9% ↓
4	62	1.47	9.6% ↓
5	79	1.36	7.0% ↓
6	97	1.29	5.4% ↓
7	204	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 187

✅ Fitting complete.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 11.09 seconds

📏 Goodness-of-fit (reduced χ²): 1.29

📏 R-factor (Rf): 5.63%

📏 R-factor squared (Rf²): 5.27%

📏 Weighted R-factor (wR): 4.41%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↓
2	lbco	atom_site	La	adp_iso	0.5000	0.5051	1216.7409	Ų	1.02 % ↑
3	lbco	atom_site	Ba	adp_iso	0.5000	0.5048	1977.3028	Ų	0.96 % ↑
4	lbco	atom_site	Co	adp_iso	0.5000	0.2371	0.0612	Ų	52.59 % ↓
5	lbco	atom_site	O	adp_iso	0.5000	1.3935	0.0167	Ų	178.71 % ↑
6	hrpt	linked_phases	lbco	scale	7.2120	9.1350	0.0641		26.66 % ↑
7	hrpt	peak		broad_gauss_u	0.0803	0.0816	0.0031	deg²	1.63 % ↑
8	hrpt	peak		broad_gauss_v	-0.1029	-0.1159	0.0067	deg²	12.62 % ↑
9	hrpt	peak		broad_gauss_w	0.1077	0.1204	0.0033	deg²	11.88 % ↑
10	hrpt	peak		broad_lorentz_y	0.0893	0.0844	0.0021	deg	5.47 % ↓
11	hrpt	instrument		twotheta_offset	0.6231	0.6226	0.0010	deg	0.09 % ↓
12	hrpt	background	10	y	167.5167	168.5585	1.3671		0.62 % ↑
13	hrpt	background	30	y	166.7627	164.3357	0.9992		1.46 % ↓
14	hrpt	background	50	y	170.8330	166.8881	0.7388		2.31 % ↓
15	hrpt	background	110	y	172.2546	175.4004	0.6571		1.83 % ↑
16	hrpt	background	165	y	180.6405	174.2811	0.9113		3.52 % ↓

⚠️ Red uncertainty: exceeds the fitted value (consider adding constraints)                                                        

Plot Measured vs Calculated¶

In [61]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [62]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Save Project State¶

In [63]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 4/5¶

Set Constraints¶

Set aliases for parameters.

In [64]:

project.analysis.aliases.create(
    label='biso_La',
    param=project.structures['lbco'].atom_sites['La'].adp_iso,
)
project.analysis.aliases.create(
    label='biso_Ba',
    param=project.structures['lbco'].atom_sites['Ba'].adp_iso,
)

project.analysis.aliases.create( label='biso_La', param=project.structures['lbco'].atom_sites['La'].adp_iso, ) project.analysis.aliases.create( label='biso_Ba', param=project.structures['lbco'].atom_sites['Ba'].adp_iso, )

Set constraints.

In [65]:

project.analysis.constraints.create(expression='biso_Ba = biso_La')

project.analysis.constraints.create(expression='biso_Ba = biso_La')

Show defined constraints.

In [66]:

project.analysis.display.constraints()

project.analysis.display.constraints()

User defined constraints

	expression
1	biso_Ba = biso_La

Constraints enabled: True

Show free parameters.

In [67]:

project.analysis.display.free_params()

project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	lbco	cell		length_a	3.89087	0.00004	-inf	inf	Å
2	lbco	atom_site	La	adp_iso	0.50509	1216.74090	-inf	inf	Ų
3	lbco	atom_site	Ba	adp_iso	0.50481	1977.30283	-inf	inf	Ų
4	lbco	atom_site	Co	adp_iso	0.23707	0.06119	-inf	inf	Ų
5	lbco	atom_site	O	adp_iso	1.39354	0.01668	-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	9.13503	0.06407	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08157	0.00314	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.11592	0.00672	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.12045	0.00328	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08445	0.00215	-inf	inf	deg
11	hrpt	instrument		twotheta_offset	0.62258	0.00104	-inf	inf	deg
12	hrpt	background	10	y	168.55849	1.36709	-inf	inf
13	hrpt	background	30	y	164.33571	0.99917	-inf	inf
14	hrpt	background	50	y	166.88814	0.73884	-inf	inf
15	hrpt	background	110	y	175.40040	0.65706	-inf	inf
16	hrpt	background	165	y	174.28113	0.91128	-inf	inf

Run Fitting¶

In [68]:

project.analysis.fit()
project.analysis.display.fit_results()

project.analysis.fit() project.analysis.display.fit_results()

Standard fitting

📋 Using experiment 🔬 'hrpt' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	1.29
2	20	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 19

✅ Fitting complete.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 1.14 seconds

📏 Goodness-of-fit (reduced χ²): 1.29

📏 R-factor (Rf): 5.63%

📏 R-factor squared (Rf²): 5.27%

📏 Weighted R-factor (wR): 4.41%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
2	lbco	atom_site	La	adp_iso	0.5051	0.5051	0.0278	Ų	0.00 % ↓
3	lbco	atom_site	Co	adp_iso	0.2371	0.2370	0.0564	Ų	0.03 % ↓
4	lbco	atom_site	O	adp_iso	1.3935	1.3935	0.0160	Ų	0.00 % ↑
5	hrpt	linked_phases	lbco	scale	9.1350	9.1351	0.0538		0.00 % ↑
6	hrpt	peak		broad_gauss_u	0.0816	0.0816	0.0031	deg²	0.00 % ↑
7	hrpt	peak		broad_gauss_v	-0.1159	-0.1159	0.0066	deg²	0.00 % ↑
8	hrpt	peak		broad_gauss_w	0.1204	0.1204	0.0032	deg²	0.00 % ↑
9	hrpt	peak		broad_lorentz_y	0.0844	0.0844	0.0021	deg	0.00 % ↓
10	hrpt	instrument		twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
11	hrpt	background	10	y	168.5585	168.5585	1.3669		0.00 % ↓
12	hrpt	background	30	y	164.3357	164.3357	0.9990		0.00 % ↓
13	hrpt	background	50	y	166.8881	166.8881	0.7386		0.00 % ↓
14	hrpt	background	110	y	175.4004	175.4006	0.6488		0.00 % ↑
15	hrpt	background	165	y	174.2811	174.2812	0.8944		0.00 % ↑

Plot Measured vs Calculated¶

In [69]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [70]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Save Project State¶

In [71]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 5/5¶

Set Constraints¶

Set more aliases for parameters.

In [72]:

project.analysis.aliases.create(
    label='occ_La',
    param=project.structures['lbco'].atom_sites['La'].occupancy,
)
project.analysis.aliases.create(
    label='occ_Ba',
    param=project.structures['lbco'].atom_sites['Ba'].occupancy,
)

project.analysis.aliases.create( label='occ_La', param=project.structures['lbco'].atom_sites['La'].occupancy, ) project.analysis.aliases.create( label='occ_Ba', param=project.structures['lbco'].atom_sites['Ba'].occupancy, )

Set more constraints.

In [73]:

project.analysis.constraints.create(
    expression='occ_Ba = 1 - occ_La',
)

project.analysis.constraints.create( expression='occ_Ba = 1 - occ_La', )

Show defined constraints.

In [74]:

project.analysis.display.constraints()

project.analysis.display.constraints()

User defined constraints

	expression
1	biso_Ba = biso_La
2	occ_Ba = 1 - occ_La

Constraints enabled: True

Set structure parameters to be refined.

In [75]:

project.structures['lbco'].atom_sites['La'].occupancy.free = True

project.structures['lbco'].atom_sites['La'].occupancy.free = True

Show free parameters after selection.

In [76]:

project.analysis.display.free_params()

project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	lbco	cell		length_a	3.89087	0.00004	-inf	inf	Å
2	lbco	atom_site	La	occupancy	0.50000		-inf	inf
3	lbco	atom_site	La	adp_iso	0.50508	0.02777	-inf	inf	Ų
4	lbco	atom_site	Co	adp_iso	0.23699	0.05643	-inf	inf	Ų
5	lbco	atom_site	O	adp_iso	1.39355	0.01599	-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	9.13509	0.05380	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08157	0.00310	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.11593	0.00664	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.12045	0.00325	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08445	0.00214	-inf	inf	deg
11	hrpt	instrument		twotheta_offset	0.62258	0.00103	-inf	inf	deg
12	hrpt	background	10	y	168.55849	1.36685	-inf	inf
13	hrpt	background	30	y	164.33569	0.99900	-inf	inf
14	hrpt	background	50	y	166.88808	0.73857	-inf	inf
15	hrpt	background	110	y	175.40056	0.64879	-inf	inf
16	hrpt	background	165	y	174.28124	0.89439	-inf	inf

Run Fitting¶

In [77]:

project.analysis.fit()
project.analysis.display.fit_results()
project.display.plotter.plot_param_correlations()

project.analysis.fit() project.analysis.display.fit_results() project.display.plotter.plot_param_correlations()

Standard fitting

📋 Using experiment 🔬 'hrpt' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	1.29
2	55	1.28

🏆 Best goodness-of-fit (reduced χ²) is 1.28 at iteration 54

✅ Fitting complete.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 2.90 seconds

📏 Goodness-of-fit (reduced χ²): 1.28

📏 R-factor (Rf): 5.61%

📏 R-factor squared (Rf²): 5.25%

📏 Weighted R-factor (wR): 4.39%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
2	lbco	atom_site	La	occupancy	0.5000	0.5840	0.0203		16.81 % ↑
3	lbco	atom_site	La	adp_iso	0.5051	0.5983	0.0355	Ų	18.46 % ↑
4	lbco	atom_site	Co	adp_iso	0.2370	0.1665	0.0580	Ų	29.74 % ↓
5	lbco	atom_site	O	adp_iso	1.3935	1.3491	0.0192	Ų	3.19 % ↓
6	hrpt	linked_phases	lbco	scale	9.1351	8.9057	0.0761		2.51 % ↓
7	hrpt	peak		broad_gauss_u	0.0816	0.0812	0.0031	deg²	0.43 % ↓
8	hrpt	peak		broad_gauss_v	-0.1159	-0.1154	0.0066	deg²	0.48 % ↓
9	hrpt	peak		broad_gauss_w	0.1204	0.1203	0.0032	deg²	0.14 % ↓
10	hrpt	peak		broad_lorentz_y	0.0844	0.0846	0.0021	deg	0.18 % ↑
11	hrpt	instrument		twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
12	hrpt	background	10	y	168.5585	168.9780	1.3666		0.25 % ↑
13	hrpt	background	30	y	164.3357	164.0535	0.9992		0.17 % ↓
14	hrpt	background	50	y	166.8881	166.9125	0.7364		0.01 % ↑
15	hrpt	background	110	y	175.4006	175.2699	0.6479		0.07 % ↓
16	hrpt	background	165	y	174.2812	174.5580	0.8935		0.16 % ↑

Plot Measured vs Calculated¶

In [78]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt')

In [79]:

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

project.display.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41)

Save Project State¶

In [80]:

project.save_as(dir_path='lbco_hrpt', temporary=True)

project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Step 5: Summary¶

This final section shows how to review the results of the analysis.

Show Project Summary¶

In [81]:

project.summary.show_report()

project.summary.show_report()

————————————
PROJECT INFO
————————————

Title

La0.5Ba0.5CoO3 at HRPT@PSI

Description

This project demonstrates a standard refinement of
La0.5Ba0.5CoO3, which crystallizes in a perovskite-type
structure, using neutron powder diffraction data collected
in constant wavelength mode at the HRPT diffractometer
(PSI).
—————————————————————
CRYSTALLOGRAPHIC DATA
—————————————————————

Phase datablock

🧩 lbco

Space group

P m -3 m

	Parameter	Value	Uncertainty
1	a	3.89086945	0.00003789
2	b	3.89086945	0.00003789
3	c	3.89086945	0.00003789
4	α	90.00000000
5	β	90.00000000
6	γ	90.00000000

Atom sites

	label	type	x	y	z	occ	Biso
1	La	La	0.00000000	0.00000000	0.00000000	0.58403384	0.59831560
2	Ba	Ba	0.00000000	0.00000000	0.00000000	0.41596616	0.59831560
3	Co	Co	0.50000000	0.50000000	0.50000000	1.00000000	0.16651452
4	O	O	0.00000000	0.50000000	0.50000000	1.00000000	1.34913985

———————————
EXPERIMENTS
———————————

Experiment datablock

🔬 hrpt

Experiment type

powder, neutron, constant wavelength bragg

Calculation engine

cryspy

Wavelength

1.49400

2θ offset

0.62261

Profile type

pseudo-voigt

Peak broadening (Gaussian)

	Parameter	Value	Uncertainty
1	U	0.08122192	0.00308943
2	V	-0.11536597	0.00662351
3	W	0.12027587	0.00324176

Peak broadening (Lorentzian)

	Parameter	Value	Uncertainty
1	X	0.00000000
2	Y	0.08459741	0.00214065

———————
FITTING
———————

Minimization engine

lmfit

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	1.28